{"paper":{"title":"Dynamics of the Universal Area-Preserving Map Associated with Period Doubling: Hyperbolic Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Denis Gaidashev, Tomas Johnson","submitted_at":"2009-05-09T09:33:41Z","abstract_excerpt":"It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\\fR}^2$. A renormalization approach has been used in \\cite{EKW1} and \\cite{EKW2} in a computer-assisted proof of existence of a \"universal\" area-preserving map $F_*$ -- a map with orbits of all binary periods $2^k, k \\in \\fN$. In this paper, we consider maps in some neighbourhood of $F_*$ and study their dynamics.\n  We first demonstrate that the map $F_*$ admits a \"bi-infinite heteroclinic tangle\": a sequence of periodic points $\\{z_k\\}$, $k \\in \\fZ$, |z_k| \\conve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.1390","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}